To this I would add: the central difficulty of this sometimes-recalcitrant piece of pedagogy, which you mostly acknowledge near the beginning of your essay, is a difference of opinion about what a real number *is. *The typical resistant non-unitarian is resistant due to a conviction that the number *is* a sequence of digits. Notice, for example frequent confusing amateur claims that sqrt(2) or pi "goes on forever" or "is infinite", while most mathematicians would insist that it was only the *decimal representation* that goes on forever. To a non-unitarian, the representation *is* the number. Convincing a person like that to abandon a very concrete reality in favor of a difficult-to-explain abstraction is the real challenge here, and I don't think your essay will win over many. On Tue, Apr 11, 2017 at 6:24 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Diagram following "Here’s how he would represent what you get when you add 0.999… to itself:" fails to open under iMac/El Capitan/Safari .
Endnotes section Q2 : I didn't understand ?!
I feel that the article circles around the topic at length, without ever clearly making what I consider the central point: that decimal notation etc. are naming conventions for denoting numbers, and --- just as with names for people --- the mapping between the two classes may be neither injective nor surjective.
The resulting ambiguity must be resolved by context; its justification lies in facilitating logical manipulation (computation) with the (abstract) entities being referenced.
WFL
On 4/11/17, James Propp <jamespropp@gmail.com> wrote:
I started writing a new draft titled "More about .999..." and would appreciate feedback. I plan on publishing it on April 17. Suggestions for references, and comments of all kinds, are welcome.
Keep in mind that all math-fun feedback goes into one mail-feed, so I won't know whose feedback is whose unless you sign your comment. Also, all substantive suggestions that I use will be acknowledged (unless you specifically ask me not to do this).
Please leave your feedback here: https://mathenchant.wordpress.com?p=1591&shareadraft=58ebef1e6b78a
Title: More about .999… Beginning: I thought my last essay on .999... was pretty good until I asked some of my students what they got out of it; then I got a humbling jolt of pedagogical reality. The students agreed that .999... is the limit of the sequence .9, .99, .999, etc., and they also agreed that the limit of that sequence i... Read more: https://mathenchant.wordpress.com?p=1591&shareadraft= 58ebef1e6b78a Thanks, jamespropp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun